and hence parametrizes the source term in units of \(\chi T^3\) .
Here, the factor \(17/37\)  simply ensures that the source term enters the transport equation with an overall numerical prefactor of \(17/37 \times 111/34 = 3/2\)  [1]}.
In order to estimate the temperature dependence of \(\theta _{\rm w}\left(T\right)\) , we will use the analytical one-loop result in Ref. [2]}, which is based on the dimensionally reduced effective thermal field theory description of the Standard Model,
\(\cos ^2 \theta _{\rm w}\left(T\right) = \cos ^2 \theta _{\rm w}\left(T=0\right) \left[1 + \frac{11}{6\pi }\,\sin ^2 \theta _{\rm w}\left(T=0\right)\,\frac{g_L T}{v\left(T\right)}\right] \,.\) 
